Introduction

Tycho Brahe (1546–1601), usually referred to as Tycho (the Latinization of his given name Tyge), was a Danish nobleman who chose to pursue his passion for astronomy rather than the career of statesman that his birth destined him for. He spent his most productive years as an astronomer on the island of Hven in the Øresund (now called Ven and part of Sweden since 1658), granted to him in fee by king Frederick II of Denmark. On the island, thanks to the financial support of the king, Tycho built Uraniborg, a residence fitted with observatories and other features designed for scientific work, and later Stjerneborg, a partially underground observatory.

Tycho Brahe

Tycho Brahe

Dedicated to achieving the highest data quality, Tycho designed new astronomical instruments and supervised their construction. With his assistants, he gathered a wealth of observations of the stars, sun, moon, and planets whose accuracy far surpassed anything available at the time.

Tycho's fortunes changed after the death of king Frederick. The new king Christian IV didn't share his father's favorable disposition towards the astronomer and several events conspired to force Tycho to leave the island and then Denmark in 1597. He ended up imperial astronomer at the court of Rudolph II in Prague where he was joined by Johannes Kepler, forced to leave his position in Graz due to religious tensions. After Tycho's death in 1601, Kepler succeeded him as imperial astronomer. He inherited Tycho's observations of the planets that enabled him to discover his famous laws of planetary motion.

For details on Tycho's life and work, refer for instance to Kitty Ferguson's book [2], the more detailed biography by J. L. E. Dreyer [8], or the comprehensive and more recent biography by Victor Thoren [5].

This page focuses on the star catalog that resulted from Tycho's measurements of star positions. Two main versions of the catalog exist.

☞ One version, containing 777 entries, is included in the first volume of Tycho's Astronomiæ Instauratæ Progymnasmata [12, pp. 258–272], published posthumously by Kepler in Prague in 1602. There also exists a 1610 edition [12], published in Frankfurt, where the star catalog exhibits some differences with the 1602 version. The 1602 version is reproduced in Tome II of Dreyer's edition of Tycho's complete works [6, pp. 258–280].

☞ Shortly before leaving Uraniborg, Tycho rushed the completion of the catalog to 1000 stars, the benchmark number set by Ptolemy whose catalog contains 1028 entries. Due to the chaotic circumstances surrounding the move, the extended 1004 entries catalog is not up to the standard of quality of the smaller one. Nevertheless, Tycho had elegant manuscript copies made of it and sent to potential new patrons in order to gain their favor. This catalog is reproduced in Tome III of Dreyer's edition of Tycho's complete works [5, pp. 344–373].

Kepler included a version of Tycho's long catalog in his last major work, Tabulæ Rudolphinæ [10, pp. 105–114]. This version is reproduced in Francis Baily's The Catalogues of Ptolemy, Ulugh Beigh, Tycho Brahe, Halley, Hevelius, Deduced from the Best Authorities [8, pp. 127–165].

Flamsteed included a copy of Tycho's catalog in the third volume of his Historia Cœlestis Britannica [9, pp. 24–45]. This appears to be a version of the long catalog, although some of the constellations are restricted to the stars included in the short one. Flamsteed's own star catalog includes cross-references to Tycho's (to be analyzed).

More recently, Dennis Rawlins in DIO 3 [3] published a version of the manuscript catalog, with some corrections, and critically examined it, going back to Tycho's original observations in order to explain inaccuracies. He also showed in great detail in DIO 2.1 [4] that some of the last entries added to the catalog in order to reach the magic count of 1000 have not been directly observed but adapted from Ptolemy's catalog.

Tycho's catalogs have already been digitized by F. Verbunt and R. H. van Gent [1] from Dreyer's and Kepler's copies and made available as VizieR's catalog J/A+A/516/A28.

I have independently digitized a few versions Tycho's catalog anyway and made the results available on this page. I copied Tycho's Manuscript catalog from Dreyer [6], the 777 star catalog from the 1602 edition of Progymnasmata [13], the 1610 edition of Progymnasmata [12], and from Dreyer [7], Kepler's version from Tabulæ Rudolphinæ [11] and Baily's collection [9], and Flamsteed's version from Historia Cœlestis Britannica [10].

Catalog data

The files tycho_*.dat contain the versions of Tycho's star catalog. For completeness and by respect for the originals, they include the star descriptions in Latin. The descriptions are UTF-8 encoded for accented and other non-ASCII characters.

File name Explanation
ReadMe File descriptions
tycho_m.dat Manuscript catalog of 1004 stars from Dreyer
tycho_t.dat Catalog of 777 stars from Progymnasmata (1602 edition)
tycho_y.dat Catalog of 777 stars from Progymnasmata (1610 edition)
tycho_d.dat Dreyer's version of the Progymnasmata catalog
tycho_k.dat Catalog of 1005 stars from Kepler's Tabulæ Rudolphinæ
tycho_b.dat Baily's version of the Tabulæ Rudolphinæ catalog
tycho_z.dat Flamsteed's version of the long catalog
notes.dat Notes on Tycho's catalogs

The ReadMe file describes the common file format of the catalog files according to the conventions for catalog descriptions of the VizieR service, with the following caveat: the VizieR standard and their Anafile package for automatic validation only accept ASCII input. Therefore, to properly match the file descriptions and pass automatic validation, the catalog files should be stripped of file descriptions, which can easily be accomplished with command-line tools. To avoid clutter, I haven't included stripped versions.

The versions of the Progymnasmata catalog differ from each other. Some position and magnitude values are missing in the 1602 version, which is clear in the [BSL02] copy. In the [LOC02] copy, these values appear to have been added by hand. The missing values are supplied in an Errata Typographica section at the end of the book, and sometimes differ from the [LOC02] handwritten values. I have followed the errata. The 1610 version has no missing values (although the errata section hasn't been updated), but differs from the 1602 version in quite a few places. Dreyer's version shows a single non-documented difference with (my interpretation of) the 1602 version. All the differences are described in notes.dat file and formalized in the corrections files.

The Kepler and Baily versions differ from each other as well. Baily has corrected some obvious errors in Kepler's version but also introduced typos of his own. The differences are described in notes.dat as well and formalized in the corrections files described below.

Besides omitting some stars from the Manuscript version, Flamsteed's version shows several differences in positions or magnitudes. I have not attempted to analyze or document them.

Constellations

The Progymnasmata and Manuscript versions start with the Zodiacal constellations, then the Northern and Southern ones. Kepler's version starts with the Northern constellations, then the Zodiacal ones, then the Southern.

The catalog covers Ptolemy's constellations except the southernmost ones (Lupus, Ara, Corona Australis, Piscis Austrinus), invisible or barely visible at Uraniborg's latitude. A handful of Centaurus stars are present as an afterthought in the Manuscript and Kepler versions. Ptolemy's order is respected within each group (Northern, Zodiacal, Southern).

In addition, the catalog features the new constellations Coma Berenices and Antinous (previously part of Leo and Aquila respectively), introduced by Caspar Vopel on a celestial globe in 1536. Coma Berenices figures between Auriga and Ophiuchus in the Progymnasmata version, but between Boötes and Corona Borealis in the Manuscript version, and as the last Northern constellation in Kepler's version.

Some constellations are designated by ancient or alternative names. These cases are collected in the following table.

Standard name Tycho Kepler
Ursa Minor Ursa Minor, Cynosura Ursa Minor, Cynosura
Ursa Major Ursa Maior, Helice Ursa Maior, Helice
Boötes Bootes seu Actophylax Bootes, Actophylax
Corona Borealis Corona Borea, Gnossia Corona Borea
Hercules Hercules, En Gonasi Engonasi, Hercules
Lyra Lyra, Vultur Cadens
Cygnus Olor, Cygnus
Cassiopeia Cassiopea
Auriga Erichthonius Auriga, Heniochus, Ericthonius
Ophiuchus Ophiuchus, Serpentarius
Serpens Serpens Ophiuchi
Sagitta Sagitta sive Telum
Aquila Vultur Aquila seu Vultur Volans
Equuleus Equuleus, Equi Sectio
Pegasus Pegasus, Equus Alatus
Triangulum Triangulus Triangulus, Deltoton
Cetus Cete Cete
Canis Minor Canis Minor, Procyon
Argo Navis Argus
Centaurus Centaurus, Chiron

Nebulous objects

The entries marked nebulous in Tycho's catalog are collected in the following table. Of these, only Cnc 1 corresponds to an actual non-star object, although the position given by Tycho corresponds very accurately to the individual member HR 3428 of this cluster.

Tycho designationModern designation
Cap 510 Cap π
Cap 612 Cap ο
Cap 87 Cap ρ
Cnc 1Open cluster Praesepe, M44, NGC 2632
Her 20HR 6641

Corrections

The correction files listed below serve two purposes. The first one is to reconcile the versions of the Progymnasmata catalog (choosing the 1602 version from Progymnasmata with errata as reference), and to reconcile Kepler's and Baily's versions of the Tabulæ Rudolphinæ catalog (choosing the version from Tabulæ Rudolphinæ as reference).

File name Explanation
corrs_m.dat Corrections to the Manuscript catalog from Dreyer
corrs_t.dat Corrections to the Progymnasmata catalog (1602 edition)
corrs_y.dat Corrections to the Progymnasmata catalog (1610 edition)
corrs_d.dat Corrections to Dreyer's version of the Progymnasmata catalog
corrs_k.dat Corrections to the Tabulæ Rudolphinæ catalog
corrs_b.dat Corrections to Baily's version of the Tabulæ Rudolphinæ catalog

The second purpose is to correct obvious position errors (wrong longitude zodiac sign or latitude sign in most cases), which Baily has done in many cases while introducing typos of his own, so that they don't make the maps on the next page (which use the corrected data) messier than they need to be.

Each entry in the correction files mentions the star designations and the corrected field values; they don't repeat unaffected field values. Consequently, they don't contain full catalog entries but rather overlays to catalog entries. Nevertheless, the correction files are described in ReadMe and they conform to the same format as the catalog files.

Star designations

Up to 4 designations are assigned to every entry in the catalog files: the sequence number mno in the Manuscript catalog, the sequence number tno in the Progymnasmata catalog, the sequence number kno in Kepler's catalog, and the combination tid of a constellation abbreviation tcon and a sequence number tnum within the constellation. These designations are not present in the originals (except Baily's version) but are more convenient than the star descriptions to identify stars uniquely.

The catalog files are sorted by the global sequence number corresponding to their source. The sequence numbers tnum by constellation are somewhat arbitrary: they follow the order of the catalogs when possible, but there are some variations between versions and these numbers may not appear sequential in some versions.

All the entries in the Progymnasmata catalog are contained in the Manuscript and Kepler versions, but both the Manuscript and Kepler versions have a handful of entries absent from the others. These cases are described at the end of notes.dat. As a result, the combination tid of constellation abbreviation and number within the constellation is the only one of the designations that can serve as global primary key for all versions.

Baily's version uses the kno and tid designations explicitly in the same manner. VizieR catalog J/A+A/516/A28 has a similar numbering scheme. My mno and tno are equivalent to theirs, but their version of kno and tid do not exactly match mine or Baily's. The main reason is that, for some lines of Kepler's catalog, they have decided differently whether to treat them as separate entries. They end up with 1004 entries in Kepler's version and Baily with 1005. I have followed Baily.

Star identifications

Dreyer's version of the Manuscript catalog and Baily's version of Kepler's catalog assign Bayer, Flamsteed, or other designations to Tycho stars. VizieR catalog J/A+A/516/A28 assigns Hipparcos catalog numbers. Rawlins's version assigns Bright Star numbers as well as Bayer and Flamsteed designations. Flamsteed's version adds Bayer letters assignments and Flamsteed's own catalog implies associations with Flamsteed designations.

File name Explanation
ident_m.dat Star identifications according to the Manuscript catalog from Dreyer
ident_b.dat Star identifications according to Kepler's catalog from Baily
ident_z.dat Star identifications according to Flamsteed's version of the long catalog
ident_f.dat Star identifications according to Flamsteed's own catalog
ident_a.dat Star identifications according to VizieR catalog J/A+A/516/A28
ident_r.dat Star identifications according to Rawlins [3]
ident_o.dat Star identifications retained for the maps
dups_o.dat Duplicate entries according to ident_o.dat

The files ident_*.dat summarize all these associations. The file format is described in ReadMe and they are subject to automatic validation.

The file ident_o.dat collects the identifications that I have retained (in general Rawlins's, unless the distance from Tycho's position to the intended star is too large) for the maps on the next page.

Duplicate entries

The file dups_o.dat lists all the pairs of duplicate entries found in Tycho's catalogs, according to the identifications file ident_o.dat. Had I used Rawlins's version, the only difference would have been about Cyg 23 and Cyg 24 which he identifies with Cyg 11 along with Cyg 25.

In dups_o.dat, there are only two pairs of duplicate entries in the Progymnasmata catalog, namely Cap 26 = Cap 27, and Oph 12 = Oph 14.

Summary Files

The file pos_all.dat summarizes the (corrected) star positions from the three main versions (Manuscript, Progymnasmata, Kepler) making commonalities and differences immediately visible. The file mag_all.dat does the same thing for star magnitudes, ignoring the magnitude dots in the Progymnasmata version..

File name Explanation
pos_all.dat Summary of star positions
mag_all.dat Summary of star magnitudes
problems.dat Summary of problem stars

Finally, the file problems.dat lists the "problem" stars in Tycho's catalog, namely the stars which have a note in Dreyer's, Baily's, or Rawlins's version or for which the distance from the catalog's position to the intended star according to ident_o.dat is larger than 6 minutes of arc.

Accuracy of the catalog

The file dists_mo.dat gives the differences between Tycho's positions (according to the Manuscript version from Dreyer) and the modern positions of the corresponding stars (according to ident_o.dat) from the Hipparcos catalog (or the SAO catalog if there is no Hipparcos match) adjusted to Tycho's epoch and equinox. Its file format is described in ReadMe.

File name Explanation
dists_mo.dat Differences between Tycho's positions and modern ones

The file gives the differences in ecliptic longitude (multiplied by the cosine of the latitude for normalization), the differences in ecliptic latitude, and the great circle distances, all in minutes of arc. The corresponding histograms below give a general idea of the overall accuracy of the catalog (data outside the range of the x axis has been discarded).

Longitude Latitude Distance
Longitude
          differences Latitude
          differences Distances

Verbunt & van Gent [1] includes similar diagrams and a detailed statistical discussion. As in the case of Ptolemy's catalog, I just note the position of the peak of the distance histogram, at about 2 arcminutes, as a measure of the catalog's general accuracy. Comparing with the corresponding value of 30 arcminutes for Ptolemy's catalog, we could say that the accuracy of Tycho's catalog is about 15 times better than Ptolemy's.

References

[1] F. Verbunt & R. H. van Gent, Three editions of the star catalogue of Tycho Brahe, Astronomy & Astrophysics 516, A28 (2010).

[2] Kitty Ferguson, Tycho and Kepler: The Unlikely Partnership that Forever Changed our Understanding of the Heavens, New York: Walker & Company, 2004.

[3] Dennis Rawlins, Tycho’s Star Catalog, DIO, Vol. 3, October 1993.

[4] Dennis Rawlins, Tycho 1004-Star Catalog's Completion Was Faked, DIO, Vol. 2, No. 1, April 1992.

[5] Victor E. Thoren, The Lord of Uraniborg: A Biography of Tycho Brahe, Cambridge University Press, 1991.

[6] John Louis Emil Dreyer, Tychonis Brahe Dani Scripta Astronomica, Tomus III, Hauniae in Libraria Gyldenlaliana, 1916.

[7] John Louis Emil Dreyer, Tychonis Brahe Dani Scripta Astronomica, Tomus II, Hauniae in Libraria Gyldenlaliana, 1913.

[8] John Louis Emil Dreyer, Tycho Brahe: a picture of scientific life and work in the sixteenth century, Edinburgh : Adam & Charles Black, 1890.

[9] Francis Baily, The Catalogues of Ptolemy, Ulugh Beigh, Tycho Brahe, Halley, Hevelius, Deduced from the Best Authorities. With Various Notes and Corrections, and a Preface to Each Catalogue. To Which is Added the Synonym of each Star, in the Catalogues of Flamsteed of Lacaille, as far as the same can be ascertained. Memoirs of the Royal Astronomical Society, Vol. 13, London, 1843. Also available here.

[10] John Flamsteed, Historia Cœlestis Britannica, Tribus Voluminus contenta. Volumen Tertium, London, 1725.

[11] Johannes Kepler, Tabulæ Rudolphinæ, Ulm: Jonas Saur, 1627.

[12] Tycho Brahe, Astronomiae Instauratae Progymnasmata, Frankfurt: Gottfried Tampach, 1610. I consulted the online versions of copies at e-rara [ETH10], the Bavarian State Library [BSL10], and the Lyon Public Library [LPL10].

[13] Tycho Brahe, Astronomiae Instauratae Progymnasmata, Uraniborg & Prague, 1602. I consulted the online versions of copies at the Library of Congress [LOC02] and the Bavarian State Library [BSL02].


Acknowledgments.

  • This research has made use of the VizieR catalogue access tool, CDS, Strasbourg, France. The original description of the VizieR service was published in A&AS 143, 23.
  • This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France.
  • Illustration: Tycho Brahe. Line engraving after T. Gemperlin, 1586. Credit: Wellcome Collection. CC BY